add feature: poisson regression point estimates bias correction

[caibengbu]

This pull request adds a new feature of point estimates bias correction for three-way network poisson regressions. It produces the same result as the stata package ppml_fe_bias. There's also some major modifications to the function in terms of formula parsing and data frame sorting.

TO-DO: add standard error correction as introduced in Weidner and Zylkin (2020)

[codecov[bot]]

Codecov Report

Merging #29 (d63388a) into master (7021ddf) will decrease coverage by 20.95%. The diff coverage is 0.00%.

@@             Coverage Diff             @@
##           master      #29       +/-   ##
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- Coverage   67.30%   46.35%   -20.96%     
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  Files          13       13               
  Lines         624      906      +282     
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  Hits          420      420               
- Misses        204      486      +282     

Impacted Files	Coverage Δ
src/GLFixedEffectModels.jl	0.00% <ø> (ø)
src/utils/biascorr.jl	0.00% <0.00%> (ø)

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[caibengbu]

There are also some minor discrepancies between the Stata package Weidner and Zylkin (2020) produced (ppml_fe_bias) and their paper:

1. In their Appendix A.2.1 Analytical Bias Correction Formula, the construction of B hat and D hat always excludes the term where i == j. In ppml_fe_bias, they include the excluded term.
2. Also in A.2, there is a strange sign change. It is implemented as a positive sign in the code but appears to be negative in the paper. Might be a typo.

I feel like they are equally important references and can't decide which one to adhere to (especially the first discrepancy). For test purposes, I align with ppml_fe_bias for now. This version is pretty much a step-by-step implementation of the paper. There might be other shortcuts we can take to simplify our codes.

[caibengbu]

There are also some minor discrepancies between the Stata package Weidner and Zylkin (2020) produced (ppml_fe_bias) and their paper:

Update on this: Discrepancy 1 is kind of a silly question to ask since in a trade gravity model a country doesn't import/export to themselves so observations whose i==j would never show up in the data. In their paper they excluded such observations and this is a result of how the likelihood function is defined. They also said that it is okay to include if used in other scenarios where observations whose i==j is not meaningless. Discrepancy 2 is a typo in the paper.